Distributive property
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Solve 3(x + 2) = 21.
Common mix-up
In this example, a student wrote 3x + 2 = 21.
The outside 3 has multiplied x, but it still needs to multiply the 2.
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See why this works
Why multiply everything inside the brackets?
If you multiplied the x but left the other number alone, you have found a useful place to pause. The outside number counts copies of the whole group.
Copy the whole group: 3(x + 2) = 3x + 6.
Imagine three bags. Each bag contains x counters and two extra counters. Opening the bags gives you three copies of x and six extra counters. Nothing was added or lost; the same contents are just written without bags. That is what distributing does to brackets.
In 3(x + 2) = 21, the line 3x + 2 = 21 counts the extra counters from only one bag. The corrected left side is 3x + 6. You can also write 6 + 3x: changing the order of addition does not change its value.
Now solve 3x + 6 = 21. Subtract 6 from both sides to keep them equal, leaving 3x = 15. Divide both sides by 3 to get x = 5. Check in the original equation: 3(5 + 2) = 3 × 7 = 21. The check reconnects your answer to the question you started with.
There is another valid route: divide both sides of the original equation by 3 first, giving x + 2 = 7. Then subtract 2. You do not always have to expand brackets first. Here, practicing expansion helps you notice why every part of a group matters.
Keep this idea
An outside multiplier applies to every term inside the brackets. Keep both sides equal as you solve, then check in the original equation.
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